Wave-Based Control of a Nonlinear Flexible System

The motivation for this work is the control of flexible mechanical systems, such as long, light robot arms, gantry cranes, and large space structures, with an actuator at one end and a free boundary at the other. Very effective control strategies have recently been developed which are based on interpreting the actuator motion as launching mechanical “waves” (propagating motion) into the flexible system while absorbing returning “waves”. These control systems are robust to system changes and to actuator limitations. They are generic, require very little system modeling, need only local sensing, and are computationally light and easy to implement. In a flexible arm, when elastic deflections are large, frequently there is strongly nonlinear behavior. This paper investigates how such nonlinearities affect the wave-based control strategy. In summary, the news is good. It is found that errors arise only when trajectories are very demanding, and even then the errors are small. Some strategies for correcting these errors are explained: addition of a linear element at the actuator-system interface, error correction by second manoeuver, and redefinition of the waves in a less-than-optimal way. The paper presents these ideas and illustrates them with numerical simulations.